Stress computation in finite thermoviscoplasticity

In this article, a constitutive theory in the framework of continuum thermomechanics is introduced to represent the viscoplastic behavior of metals at finite deformations. In particular, the experimentally observed thermomechanical coupling phenomena are described by the theory. The model is based on the assumption that the occurring viscoplastic deformations are isochoric. For the numerical integration of the constitutive theory, a backward Euler method is applied. As a matter of fact, the application of the original backward Euler scheme does not preserve the property of the viscoplastic deformations to be isochoric. A major topic of the present article is the development of an improved numerical integrator on the basis of the original backward Euler method, which preserves exactly the incompressibility of the occurring viscoplastic deformations.